Химическая кинетика. Наумов А.В. - 12 стр.

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Ɍɨɝɞɚ ɜ ɞɪɭɝɨɣ ɱɚɫɬɢ ɨɤɚɠɟɬɫɹ ɨɬɧɨɲɟɧɢɟ ɤɨɧɫɬɚɧɬ ɫɤɨɪɨɫɬɟɣ. ɉɨɫɤɨɥɶɤɭ
k
r
ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɣ, ɩɨɫɬɨɥɶɤɭ ɢ ɢɯ ɨɬɧɨɲɟɧɢɟ K ɹɜɥɹɟɬɫɹ ɜɟ-
ɥɢɱɢɧɨɣ ɩɨɫɬɨɹɧɧɨɣ. ɗɬɨ ɨɬɧɨɲɟɧɢɟ ɧɚɡɵɜɚɟɬɫɹ
ɤɨɧɫɬɚɧɬɨɣ ɯɢɦɢɱɟɫɤɨɝɨ
ɪɚɜɧɨɜɟɫɢɹ
.
ɋɭɳɟɫɬɜɨɜɚɧɢɟ ɤɨɧɫɬɚɧɬɵ
K – ɨɫɧɨɜɧɨɣ ɡɚɤɨɧ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ
(ɟɝɨ ɬɚɤ ɠɟ ɧɚɡɵɜɚɸɬ
ɡɚɤɨɧɨɦ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ; ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ
ɩɨɞɬɜɟɪɠɞɟɧ Ƚɭɥɶɞɛɟɪɝɨɦ ɢ ȼɚɚɝɟ). Ɉɧ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɪɚɜɧɨɜɟɫɧɵɟ ɤɨɧɰɟɧ-
ɬɪɚɰɢɢ ɦɨɝɭɬ ɛɵɬɶ ɥɸɛɵɦɢ, ɧɨ ɬɚɤɢɦɢ, ɱɬɨɛɵ ɭɞɨɜɥɟɬɜɨɪɹɥɨɫɶ ɫɨɨɬɧɨɲɟ-
ɧɢɟ (I.22), ɜ ɤɨɬɨɪɨɦ
K – ɜɩɨɥɧɟ ɨɩɪɟɞɟɥɟɧɧɚɹ ɜɟɥɢɱɢɧɚ ɩɪɢ ɞɚɧɧɵɯ ɭɫɥɨ-
ɜɢɹɯ (ɬɟɦɩɟɪɚɬɭɪɟ ɢ ɞɚɜɥɟɧɢɢ). ɋɨɨɬɧɨɲɟɧɢɟ (I.22) ɭɫɬɚɧɚɜɥɢɜɚɟɬ
ɫɜɹɡɶ
ɦɟɠɞɭ
m + n = N ɩɟɪɟɦɟɧɧɵɦɢ
[
A
1
], …, [A
m
], [BB
1
], …, [B
n
B ], (I.23)
ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɬɨɥɶɤɨ
N – 1 ɢɡ ɧɢɯ ɦɨɝɭɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶɫɹ ɤɚɤ ɧɟɡɚɜɢɫɢ-
ɦɵɟ. ȼɫɟ ɫɨɫɬɨɹɧɢɹ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɷɬɨɣ ɫɜɹɡɢ, ɛɭɞɭɬ ɪɚɜɧɨɜɟɫɧɵɦɢ;
ɥɸɛɚɹ ɫɨɜɨɤɭɩɧɨɫɬɶ ɡɧɚɱɟɧɢɣ (I.23), ɧɟ ɭɞɨɜɥɟɬɜɨɪɹɸɳɚɹ ɟɣ, ɨɬɦɟɱɚɟɬ ɧɟ-
ɪɚɜɧɨɜɟɫɧɨɟ ɫɨɫɬɨɹɧɢɟ.
ɉɭɫɬɶ ɦɵ ɢɦɟɟɦ ɫɢɫɬɟɦɭ, ɧɚɯɨɞɹɳɭɸɫɹ ɜ ɪɚɜɧɨɜɟɫɢɢ. ȼɧɟɫɟɦ ɫɸɞɚ
ɦɝɧɨɜɟɧɧɨ ɧɟɤɨɬɨɪɭɸ ɞɨɛɚɜɤɭ ɨɞɧɨɝɨ ɢɡ ɜɟɳɟɫɬɜ, ɭɱɚɫɬɜɭɸɳɢɯ ɜ ɪɟɚɤɰɢɢ,
ɫɤɚɠɟɦ, ɨɞɧɨɝɨ ɢɡ ɜɟɳɟɫɬɜ
A
i
(ɫɢɫɬɟɦɚ ɜ ɤɚɤɨɣ-ɬɨ ɦɨɦɟɧɬ ɞɨɥɠɧɚ ɛɵɬɶ
ɨɬɤɪɵɬɨɣ
, ɬɨ ɟɫɬɶ ɞɨɩɭɫɤɚɬɶ ɩɟɪɟɧɨɫ ɜɟɳɟɫɬɜɚ ɢɡɜɧɟ). ȼ ɷɬɨɬ ɦɨɦɟɧɬ
ɫɨɨɬɧɨɲɟɧɢɟ (I.22) ɩɟɪɟɫɬɚɧɟɬ ɭɞɨɜɥɟɬɜɨɪɹɬɶɫɹ, ɢ ɪɚɜɧɨɜɟɫɢɟ ɧɚɪɭɲɢɬɫɹ.
ȼ ɫɢɫɬɟɦɟ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨ ɞɨɥɠɧɵ ɩɪɨɢɡɨɣɬɢ ɢɡɦɟɧɟɧɢɹ, ɜɟɞɭɳɢɟ ɤ ɬɨ-
ɦɭ, ɱɬɨɛɵ ɜɨɫɫɬɚɧɨɜɢɥɨɫɶ ɢɫɯɨɞɧɨɟ ɨɬɧɨɲɟɧɢɟ (I.22). ɋ ɤɢɧɟɬɢɱɟɫɤɨɣ ɬɨɱ-
ɤɢ ɡɪɟɧɢɹ ɜɜɟɞɟɧɢɟ ɥɸɛɨɝɨ ɢɡ ɢɫɯɨɞɧɵɯ ɜɟɳɟɫɬɜ ɜɨɡɛɭɠɞɚɟɬ ɩɪɹɦɭɸ ɪɟ-
ɚɤɰɢɸ (I.16), ɜ ɪɟɡɭɥɶɬɚɬɟ ɤɨɬɨɪɨɣ ɱɚɫɬɶ ɜɟɳɟɫɬɜ
A
i
ɢɡɪɚɫɯɨɞɭɟɬɫɹ ɢ ɭɫɬɚ-
ɧɨɜɢɬɫɹ ɧɨɜɨɟ ɫɨɫɬɨɹɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɫ ɧɨɜɵɦɢ ɡɧɚɱɟɧɢɹɦɢ (I.23). ɉɪɢ ɭɞɚ-
ɥɟɧɢɢ ɥɸɛɨɝɨ ɜɟɳɟɫɬɜɚ ɢɡ ɫɢɫɬɟɦɵ ɪɟɚɤɰɢɹ ɩɨɣɞɟɬ ɜ ɫɬɨɪɨɧɭ ɨɛɪɚɡɨɜɚɧɢɹ
ɷɬɨɝɨ ɜɟɳɟɫɬɜɚ, ɢ ɛɭɞɟɬ ɢɞɬɢ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɧɟ ɭɫɬɚɧɨɜɢɬɫɹ ɪɚɜɧɨɜɟɫɢɟ.
ɗɬɭ ɫɢɬɭɚɰɢɸ ɧɚɡɵɜɚɸɬ
ɫɦɟɳɟɧɢɟɦ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ.
ɍɪɚɜɧɟɧɢɟ (I.22) ɫɨɜɦɟɫɬɧɨ ɫɨ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɦ ɡɚɤɨɧɨɦ (I.2) ɩɨɡɜɨ-
ɥɹɟɬ ɜɵɱɢɫɥɢɬɶ ɪɚɜɧɨɜɟɫɧɵɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜɫɟɯ ɭɱɚɫɬɧɢɤɨɜ ɪɟɚɤɰɢɢ ɩɪɢ
ɥɸɛɵɯ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ
C
A
1
0
, …, C
A
m
0
, C
B
1
0
, …, C
B
n
0
. Ɉɩɢɲɟɦ ɨɛɳɢɣ
ɦɟɬɨɞ ɧɚ ɩɪɢɦɟɪɟ ɪɟɚɤɰɢɢ (I.18). ɍɪɚɜɧɟɧɢɹ ɡɚɤɨɧɚ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ ɢ
ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɝɨ ɡɚɤɨɧɚ ɢɦɟɸɬ ɜɢɞ:
[]
[]
B
K
A
, C
A
0
– [A] = [B] – C
B
0
.
ȼɬɨɪɨɟ ɢɡ ɧɢɯ, ɡɚɩɢɫɚɧɧɨɟ ɞɥɹ ɫɨɫɬɨɹɧɢɹ ɪɚɜɧɨɜɟɫɢɹ, ɜɵɪɚɠɚɟɬ ɫ ɨɯɪɚ-
ɧɟɧɢɟ
ɜɟɳɟɫɬɜɚ, ɩɟɪɜɨɟ – ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɜɟɳɟɫɬɜɚɦɟɠɞɭ ɟɝɨ ɪɚɜ-
ɧɨɜɟɫɧɵɦɢ ɮɨɪɦɚɦɢ. ɂɯ ɫɨɜɦɟɫɬɧɨɟ ɪɟɲɟɧɢɟ ɞɚɟɬ:
23
00
1
[]
AB
CC
K
A
,
00
1
[]
AB
CC
K
BK
,
ɱɬɨ ɫɨɜɩɚɞɚɟɬ ɫɨ ɡɧɚɱɟɧɢɹɦɢ [
A] ɢ [B], ɩɨɥɭɱɟɧɧɵɦɢ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɵɦ
ɪɟɲɟɧɢɟɦ ɤɢɧɟɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ.
Ɋɚɫɫɦɨɬɪɢɦ ɟɳɟ ɨɞɢɧ ɩɪɢɦɟɪ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɨ ɪɚɜɧɨɜɟɫɢɢ. ɉɭɫɬɶ ɢɦɟɟɬɫɹ ɨɛɪɚ-
ɬɢɦɵɣ ɪɚɫɩɚɞ ɫɨɟɞɢɧɟɧɢɹ XY ɩɨ ɭɪɚɜɧɟɧɢɸ
XY
ĺ
ĸ
X + Y.
ȿɫɥɢ ɨɛɨɡɧɚɱɢɬɶ ɱɟɪɟɡ D ɞɨɥɸ ɪɚɫɩɚɜɲɢɯɫɹ ɱɚɫɬɢɰ ɜ ɪɚɜɧɨɜɟɫɢɢ, ɬɨ
0
[][]
X
Y
XY C D ɢ
0
[](1)
X
Y
XY CD .
ȼɬɨɪɨɟ ɭɪɚɜɧɟɧɢɟ, ɤɚɤ ɢ ɪɚɜɟɧɫɬɜɨ [X] = [Y], ɜɵɪɚɠɚɟɬ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɟ ɨɬɧɨɲɟɧɢɹ
ɦɟɠɞɭ ɭɱɚɫɬɧɢɤɚɦɢ ɪɟɚɤɰɢɢ. ɉɨ ɡɚɤɨɧɭ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ
2
0
1
X
Y
K
C
D
D
.
ɂɡ ɞɜɭɯ ɤɨɪɧɟɣ ɷɬɨɝɨ ɤɜɚɞɪɚɬɧɨɝɨ ɩɨ D ɭɪɚɜɧɟɧɢɹ ɧɭɠɧɨ, ɪɚɡɭɦɟɟɬɫɹ, ɜɵɛɪɚɬɶ ɩɨɥɨɠɢ-
ɬɟɥɶɧɵɣ ɤɨɪɟɧɶ:

20
0
1
4
2
XY
XY
KC K
C
D .
ɉɨɫɥɟɞɧɹɹ ɮɨɪɦɭɥɚ ɩɪɢɦɟɧɢɦɚ, ɜ ɱɚɫɬɧɨɫɬɢ, ɞɥɹ ɢɨɧɢɡɚɰɢɢ ɷɥɟɤɬɪɨɥɢɬɨɜ, ɤɨɝɞɚ ɨɛɪɚ-
ɡɭɸɬɫɹ ɤɚɬɢɨɧɵ X
+
ɢ ɚɧɢɨɧɵ Y
–
. Ɉɧɚ ɢɡɜɟɫɬɧɚ ɩɨɞ ɢɦɟɧɟɦ ɡɚɤɨɧɚ ɪɚɡɛɚɜɥɟɧɢɹ Ɉɫɬ-
ɜɚɥɶɞɚ (W. Ostwald, 1888).
ɂɡ ɡɚɤɨɧɚ ɪɚɡɛɚɜɥɟɧɢɹ ɫɥɟɞɭɟɬ, ɱɬɨ ɪɚɜɧɨɜɟɫɧɚɹ ɫɬɟɩɟɧɶ ɞɢɫɫɨɰɢɚɰɢɢ (ɢɨɧɢɡɚɰɢɢ) D
ɡɚɜɢɫɢɬ ɨɬ ɧɚɱɚɥɶɧɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɪɚɫɩɚɞɚɸɳɟɝɨɫɹ ɜɟɳɟɫɬɜɚ. ɍɛɵɜɚɹ ɦɨɧɨɬɨɧɧɨ, ɨɧɚ
ɢɡɦɟɧɹɟɬɫɹ ɨɬ 1 ɜ ɩɪɟɞɟɥɟ ɩɪɢ ɞɨ ɧɭɥɹ ɜ ɩɪɟɞɟɥɟ
0
0
XY
C '
0
XY
C f' . Ɍɟɦ ɫɚɦɵɦ ɩɨɤɚɡɚ-
ɧɨ, ɱɬɨ ɩɪɢ ɛɟɫɤɨɧɟɱɧɨɦ ɪɚɡɛɚɜɥɟɧɢɢ ()ɩɪɨɢɫɯɨɞɢɬ ɩɨɥɧɵɣ ɪɚɫɩɚɞ ɜɟɳɟɫɬɜɚ.
0
0
XY
C '
Ɍɟɩɟɪɶ ɫɬɚɧɨɜɢɬɫɹ ɹɫɧɨ, ɱɬɨ ɜ ɫɥɭɱɚɟ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɨɛɪɚɬɢɦɨɣ ɪɟɚɤɰɢɢ
ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ ɥɢɛɨ ɤɪɚɣɧɟ ɜɟɥɢɤɚ, ɟɫɥɢ
k
+
# k
–
, ɥɢɛɨ ɤɪɚɣɧɟ ɦɚɥɚ,
ɟɫɥɢ
k
+
" k
–
. ȼ ɷɬɢɯ ɫɥɭɱɚɹɯ ɪɟɚɤɰɢɹ ɩɨɱɬɢ ɞɨɯɨɞɢɬ ɞɨ ɤɨɧɰɚ (ɫɥɟɜɚ ɧɚɩɪɚɜɨ
ɢɥɢ ɫɩɪɚɜɚ ɧɚɥɟɜɨ). ɇɚɩɪɢɦɟɪ, ɷɥɟɤɬɪɨɥɢɬ ɫɱɢɬɚɟɬɫɹ ɫɢɥɶɧɵɦ, ɟɫɥɢ ɟɝɨ ɤɨɧ-
ɫɬɚɧɬɚ ɢɨɧɢɡɚɰɢɢ
K ~ 10
2
. Ʉɚɤ ɦɨɠɧɨ ɭɛɟɞɢɬɶɫɹ ɩɨ ɮɨɪɦɭɥɟ Ɉɫɬɜɚɥɶɞɚ, ɬɚɤɨɣ
ɷɥɟɤɬɪɨɥɢɬ ɞɢɫɫɨɰɢɢɪɭɟɬ ɩɨɱɬɢ ɧɚɰɟɥɨ (
D ɩɪɢɛɥɢɠɚɟɬɫɹ ɤ 1).
ɇɚɤɨɧɟɰ, ɦɨɠɧɨ ɡɚɦɟɬɢɬɶ, ɱɬɨ ɜ ɫɢɬɭɚɰɢɢ ɪɚɜɧɨɜɟɫɢɹ ɜɫɟ ɧɚɲɢ ɭɪɚɜɧɟ-
ɧɢɹ ɞɨɩɭɫɤɚɸɬ ɩɪɨɱɬɟɧɢɟ ɤɚɤ ɫɥɟɜɚ ɧɚɩɪɚɜɨ, ɬɚɤ ɢ ɫɩɪɚɜɚ ɧɚɥɟɜɨ, ɩɨɫɤɨɥɶ-
ɤɭ ɬɭɬ ɧɟɬ ɜɵɞɟɥɟɧɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ ɩɪɟɜɪɚɳɟɧɢɹ. ɗɬɨ ɞɟɥɚɟɬ ɜ ɢɡɜɟɫɬɧɨɦ
ɫɦɵɫɥɟ ɭɫɥɨɜɧɵɦɢ ɩɨɧɹɬɢɹ «ɢɫɯɨɞɧɨɟ ɜɟɳɟɫɬɜɨ» ɢ «ɩɪɨɞɭɤɬ» ɪɟɚɤɰɢɢ.
ɂɬɟ, ɢ ɞɪɭɝɢɟ, ɤɚɤ ɭɠɟ ɡɚɦɟɱɟɧɨ, ɫɨɫɭɳɟɫɬɜɭɸɬ ɜ ɪɚɜɧɨɜɟɫɧɨɣ ɫɢɫɬɟɦɟ, ɢ
ɱɬɨ ɫɱɢɬɚɬɶ ɢɫɯɨɞɧɵɦ, ɚ ɱɬɨ ɩɪɨɞɭɤɬɨɦ – ɜɨɩɪɨɫ ɫɨɝɥɚɲɟɧɢɹ. ȿɫɥɢ ɫɬɟ-
ɯɢɨɦɟɬɪɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ ɩɟɪɟɩɢɫɚɬɶ ɜ ɞɪɭɝɨɣ ɨɪɢɟɧɬɚɰɢɢ, ɬɨ ɤɨɧɫɬɚɧɬɭ
ɪɚɜɧɨɜɟɫɢɹ ɫɥɟɞɭɟɬ ɡɚɦɟɧɢɬɶ ɨɛɪɚɬɧɨɣ ɜɟɥɢɱɢɧɨɣ
K
–1
.
24
Ɍɨɝɞɚ ɜ ɞɪɭɝɨɣ ɱɚɫɬɢ ɨɤɚɠɟɬɫɹ ɨɬɧɨɲɟɧɢɟ ɤɨɧɫɬɚɧɬ ɫɤɨɪɨɫɬɟɣ. ɉɨɫɤɨɥɶɤɭ                                               0
                                                                                                                  C A  CB
                                                                                                                               0                  0     0
                                                                                                                                                 C A  CB
kr ɧɟ ɡɚɜɢɫɹɬ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɣ, ɩɨɫɬɨɥɶɤɭ ɢ ɢɯ ɨɬɧɨɲɟɧɢɟ K ɹɜɥɹɟɬɫɹ ɜɟ-                                     [ A]                    ,,   [ B] K
ɥɢɱɢɧɨɣ ɩɨɫɬɨɹɧɧɨɣ. ɗɬɨ ɨɬɧɨɲɟɧɢɟ ɧɚɡɵɜɚɟɬɫɹ ɤɨɧɫɬɚɧɬɨɣ ɯɢɦɢɱɟɫɤɨɝɨ                                         K 1               K 1
                                                                                 ɱɬɨ ɫɨɜɩɚɞɚɟɬ ɫɨ ɡɧɚɱɟɧɢɹɦɢ [A] ɢ [B], ɩɨɥɭɱɟɧɧɵɦɢ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɵɦ
ɪɚɜɧɨɜɟɫɢɹ.
                                                                                 ɪɟɲɟɧɢɟɦ ɤɢɧɟɬɢɱɟɫɤɨɝɨ ɭɪɚɜɧɟɧɢɹ.
    ɋɭɳɟɫɬɜɨɜɚɧɢɟ ɤɨɧɫɬɚɧɬɵ K – ɨɫɧɨɜɧɨɣ ɡɚɤɨɧ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ
(ɟɝɨ ɬɚɤ ɠɟ ɧɚɡɵɜɚɸɬ ɡɚɤɨɧɨɦ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ; ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ                     Ɋɚɫɫɦɨɬɪɢɦ ɟɳɟ ɨɞɢɧ ɩɪɢɦɟɪ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɨ ɪɚɜɧɨɜɟɫɢɢ. ɉɭɫɬɶ ɢɦɟɟɬɫɹ ɨɛɪɚ-
ɩɨɞɬɜɟɪɠɞɟɧ Ƚɭɥɶɞɛɟɪɝɨɦ ɢ ȼɚɚɝɟ). Ɉɧ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɪɚɜɧɨɜɟɫɧɵɟ ɤɨɧɰɟɧ-           ɬɢɦɵɣ ɪɚɫɩɚɞ ɫɨɟɞɢɧɟɧɢɹ XY ɩɨ ɭɪɚɜɧɟɧɢɸ
ɬɪɚɰɢɢ ɦɨɝɭɬ ɛɵɬɶ ɥɸɛɵɦɢ, ɧɨ ɬɚɤɢɦɢ, ɱɬɨɛɵ ɭɞɨɜɥɟɬɜɨɪɹɥɨɫɶ ɫɨɨɬɧɨɲɟ-                                                   XY ĺĸ X + Y.
ɧɢɟ (I.22), ɜ ɤɨɬɨɪɨɦ K – ɜɩɨɥɧɟ ɨɩɪɟɞɟɥɟɧɧɚɹ ɜɟɥɢɱɢɧɚ ɩɪɢ ɞɚɧɧɵɯ ɭɫɥɨ-          ȿɫɥɢ ɨɛɨɡɧɚɱɢɬɶ ɱɟɪɟɡ D ɞɨɥɸ ɪɚɫɩɚɜɲɢɯɫɹ ɱɚɫɬɢɰ ɜ ɪɚɜɧɨɜɟɫɢɢ, ɬɨ
ɜɢɹɯ (ɬɟɦɩɟɪɚɬɭɪɟ ɢ ɞɚɜɥɟɧɢɢ). ɋɨɨɬɧɨɲɟɧɢɟ (I.22) ɭɫɬɚɧɚɜɥɢɜɚɟɬ ɫɜɹɡɶ                                                  0
                                                                                                        [ X ] [Y ] DC XY                       0
                                                                                                                            ɢ [ XY ] (1  D)C XY .
ɦɟɠɞɭ m + n = N ɩɟɪɟɦɟɧɧɵɦɢ
                                                                                 ȼɬɨɪɨɟ ɭɪɚɜɧɟɧɢɟ, ɤɚɤ ɢ ɪɚɜɟɧɫɬɜɨ [X] = [Y], ɜɵɪɚɠɚɟɬ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɟ ɨɬɧɨɲɟɧɢɹ
                                                                                 ɦɟɠɞɭ ɭɱɚɫɬɧɢɤɚɦɢ ɪɟɚɤɰɢɢ. ɉɨ ɡɚɤɨɧɭ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ
                             [A1], …, [Am], [B1], …, [Bn],              (I.23)
                                                                                                                                    D2 0
                                              B        B




                                                                                                                        K               C XY .
                                                                                                                                   1 D
ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɬɨɥɶɤɨ N – 1 ɢɡ ɧɢɯ ɦɨɝɭɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶɫɹ ɤɚɤ ɧɟɡɚɜɢɫɢ-
                                                                                 ɂɡ ɞɜɭɯ ɤɨɪɧɟɣ ɷɬɨɝɨ ɤɜɚɞɪɚɬɧɨɝɨ ɩɨ D ɭɪɚɜɧɟɧɢɹ ɧɭɠɧɨ, ɪɚɡɭɦɟɟɬɫɹ, ɜɵɛɪɚɬɶ ɩɨɥɨɠɢ-
ɦɵɟ. ȼɫɟ ɫɨɫɬɨɹɧɢɹ, ɭɞɨɜɥɟɬɜɨɪɹɸɳɢɟ ɷɬɨɣ ɫɜɹɡɢ, ɛɭɞɭɬ ɪɚɜɧɨɜɟɫɧɵɦɢ;              ɬɟɥɶɧɵɣ ɤɨɪɟɧɶ:
ɥɸɛɚɹ ɫɨɜɨɤɭɩɧɨɫɬɶ ɡɧɚɱɟɧɢɣ (I.23), ɧɟ ɭɞɨɜɥɟɬɜɨɪɹɸɳɚɹ ɟɣ, ɨɬɦɟɱɚɟɬ ɧɟ-                                             1
ɪɚɜɧɨɜɟɫɧɨɟ ɫɨɫɬɨɹɧɢɟ.                                                                                        D       0
                                                                                                                                   K 2  4 KC XY
                                                                                                                                              0
                                                                                                                                                 K .
                                                                                                                   2C XY
    ɉɭɫɬɶ ɦɵ ɢɦɟɟɦ ɫɢɫɬɟɦɭ, ɧɚɯɨɞɹɳɭɸɫɹ ɜ ɪɚɜɧɨɜɟɫɢɢ. ȼɧɟɫɟɦ ɫɸɞɚ
                                                                                 ɉɨɫɥɟɞɧɹɹ ɮɨɪɦɭɥɚ ɩɪɢɦɟɧɢɦɚ, ɜ ɱɚɫɬɧɨɫɬɢ, ɞɥɹ ɢɨɧɢɡɚɰɢɢ ɷɥɟɤɬɪɨɥɢɬɨɜ, ɤɨɝɞɚ ɨɛɪɚ-
ɦɝɧɨɜɟɧɧɨ ɧɟɤɨɬɨɪɭɸ ɞɨɛɚɜɤɭ ɨɞɧɨɝɨ ɢɡ ɜɟɳɟɫɬɜ, ɭɱɚɫɬɜɭɸɳɢɯ ɜ ɪɟɚɤɰɢɢ,
                                                                                 ɡɭɸɬɫɹ ɤɚɬɢɨɧɵ X + ɢ ɚɧɢɨɧɵ Y –. Ɉɧɚ ɢɡɜɟɫɬɧɚ ɩɨɞ ɢɦɟɧɟɦ ɡɚɤɨɧɚ ɪɚɡɛɚɜɥɟɧɢɹ Ɉɫɬ-
ɫɤɚɠɟɦ, ɨɞɧɨɝɨ ɢɡ ɜɟɳɟɫɬɜ Ai (ɫɢɫɬɟɦɚ ɜ ɤɚɤɨɣ-ɬɨ ɦɨɦɟɧɬ ɞɨɥɠɧɚ ɛɵɬɶ              ɜɚɥɶɞɚ (W. Ostwald, 1888).
ɨ ɬ ɤ ɪ ɵ ɬ ɨ ɣ , ɬɨ ɟɫɬɶ ɞɨɩɭɫɤɚɬɶ ɩɟɪɟɧɨɫ ɜɟɳɟɫɬɜɚ ɢɡɜɧɟ). ȼ ɷɬɨɬ ɦɨɦɟɧɬ           ɂɡ ɡɚɤɨɧɚ ɪɚɡɛɚɜɥɟɧɢɹ ɫɥɟɞɭɟɬ, ɱɬɨ ɪɚɜɧɨɜɟɫɧɚɹ ɫɬɟɩɟɧɶ ɞɢɫɫɨɰɢɚɰɢɢ (ɢɨɧɢɡɚɰɢɢ) D
ɫɨɨɬɧɨɲɟɧɢɟ (I.22) ɩɟɪɟɫɬɚɧɟɬ ɭɞɨɜɥɟɬɜɨɪɹɬɶɫɹ, ɢ ɪɚɜɧɨɜɟɫɢɟ ɧɚɪɭɲɢɬɫɹ.           ɡɚɜɢɫɢɬ ɨɬ ɧɚɱɚɥɶɧɨɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɪɚɫɩɚɞɚɸɳɟɝɨɫɹ ɜɟɳɟɫɬɜɚ. ɍɛɵɜɚɹ ɦɨɧɨɬɨɧɧɨ, ɨɧɚ
ȼ ɫɢɫɬɟɦɟ ɫɚɦɨɩɪɨɢɡɜɨɥɶɧɨ ɞɨɥɠɧɵ ɩɪɨɢɡɨɣɬɢ ɢɡɦɟɧɟɧɢɹ, ɜɟɞɭɳɢɟ ɤ ɬɨ-                                              0                          0
                                                                                 ɢɡɦɟɧɹɟɬɫɹ ɨɬ 1 ɜ ɩɪɟɞɟɥɟ ɩɪɢ C XY ' 0 ɞɨ ɧɭɥɹ ɜ ɩɪɟɞɟɥɟ C XY ' f . Ɍɟɦ ɫɚɦɵɦ ɩɨɤɚɡɚ-
ɦɭ, ɱɬɨɛɵ ɜɨɫɫɬɚɧɨɜɢɥɨɫɶ ɢɫɯɨɞɧɨɟ ɨɬɧɨɲɟɧɢɟ (I.22). ɋ ɤɢɧɟɬɢɱɟɫɤɨɣ ɬɨɱ-                                                    0
                                                                                 ɧɨ, ɱɬɨ ɩɪɢ ɛɟɫɤɨɧɟɱɧɨɦ ɪɚɡɛɚɜɥɟɧɢɢ ( C XY ' 0 ) ɩɪɨɢɫɯɨɞɢɬ ɩɨɥɧɵɣ ɪɚɫɩɚɞ ɜɟɳɟɫɬɜɚ.
ɤɢ ɡɪɟɧɢɹ ɜɜɟɞɟɧɢɟ ɥɸɛɨɝɨ ɢɡ ɢɫɯɨɞɧɵɯ ɜɟɳɟɫɬɜ ɜɨɡɛɭɠɞɚɟɬ ɩɪɹɦɭɸ ɪɟ-
ɚɤɰɢɸ (I.16), ɜ ɪɟɡɭɥɶɬɚɬɟ ɤɨɬɨɪɨɣ ɱɚɫɬɶ ɜɟɳɟɫɬɜ Ai ɢɡɪɚɫɯɨɞɭɟɬɫɹ ɢ ɭɫɬɚ-
ɧɨɜɢɬɫɹ ɧɨɜɨɟ ɫɨɫɬɨɹɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɫ ɧɨɜɵɦɢ ɡɧɚɱɟɧɢɹɦɢ (I.23). ɉɪɢ ɭɞɚ-              Ɍɟɩɟɪɶ ɫɬɚɧɨɜɢɬɫɹ ɹɫɧɨ, ɱɬɨ ɜ ɫɥɭɱɚɟ ɩɪɚɤɬɢɱɟɫɤɢ ɧɟɨɛɪɚɬɢɦɨɣ ɪɟɚɤɰɢɢ
ɥɟɧɢɢ ɥɸɛɨɝɨ ɜɟɳɟɫɬɜɚ ɢɡ ɫɢɫɬɟɦɵ ɪɟɚɤɰɢɹ ɩɨɣɞɟɬ ɜ ɫɬɨɪɨɧɭ ɨɛɪɚɡɨɜɚɧɢɹ            ɤɨɧɫɬɚɧɬɚ ɪɚɜɧɨɜɟɫɢɹ ɥɢɛɨ ɤɪɚɣɧɟ ɜɟɥɢɤɚ, ɟɫɥɢ k+ # k–, ɥɢɛɨ ɤɪɚɣɧɟ ɦɚɥɚ,
ɷɬɨɝɨ ɜɟɳɟɫɬɜɚ, ɢ ɛɭɞɟɬ ɢɞɬɢ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɧɟ ɭɫɬɚɧɨɜɢɬɫɹ ɪɚɜɧɨɜɟɫɢɟ.         ɟɫɥɢ k+ " k–. ȼ ɷɬɢɯ ɫɥɭɱɚɹɯ ɪɟɚɤɰɢɹ ɩɨɱɬɢ ɞɨɯɨɞɢɬ ɞɨ ɤɨɧɰɚ (ɫɥɟɜɚ ɧɚɩɪɚɜɨ
ɗɬɭ ɫɢɬɭɚɰɢɸ ɧɚɡɵɜɚɸɬ ɫɦɟɳɟɧɢɟɦ ɯɢɦɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ.                          ɢɥɢ ɫɩɪɚɜɚ ɧɚɥɟɜɨ). ɇɚɩɪɢɦɟɪ, ɷɥɟɤɬɪɨɥɢɬ ɫɱɢɬɚɟɬɫɹ ɫɢɥɶɧɵɦ, ɟɫɥɢ ɟɝɨ ɤɨɧ-
    ɍɪɚɜɧɟɧɢɟ (I.22) ɫɨɜɦɟɫɬɧɨ ɫɨ ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɢɦ ɡɚɤɨɧɨɦ (I.2) ɩɨɡɜɨ-         ɫɬɚɧɬɚ ɢɨɧɢɡɚɰɢɢ K ~ 102. Ʉɚɤ ɦɨɠɧɨ ɭɛɟɞɢɬɶɫɹ ɩɨ ɮɨɪɦɭɥɟ Ɉɫɬɜɚɥɶɞɚ, ɬɚɤɨɣ
ɥɹɟɬ ɜɵɱɢɫɥɢɬɶ ɪɚɜɧɨɜɟɫɧɵɟ ɤɨɧɰɟɧɬɪɚɰɢɢ ɜɫɟɯ ɭɱɚɫɬɧɢɤɨɜ ɪɟɚɤɰɢɢ ɩɪɢ              ɷɥɟɤɬɪɨɥɢɬ ɞɢɫɫɨɰɢɢɪɭɟɬ ɩɨɱɬɢ ɧɚɰɟɥɨ (D ɩɪɢɛɥɢɠɚɟɬɫɹ ɤ 1).
ɥɸɛɵɯ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ CA10, …, CAm0, CB10, …, CBn0. Ɉɩɢɲɟɦ ɨɛɳɢɣ                  ɇɚɤɨɧɟɰ, ɦɨɠɧɨ ɡɚɦɟɬɢɬɶ, ɱɬɨ ɜ ɫɢɬɭɚɰɢɢ ɪɚɜɧɨɜɟɫɢɹ ɜɫɟ ɧɚɲɢ ɭɪɚɜɧɟ-
ɦɟɬɨɞ ɧɚ ɩɪɢɦɟɪɟ ɪɟɚɤɰɢɢ (I.18). ɍɪɚɜɧɟɧɢɹ ɡɚɤɨɧɚ ɞɟɣɫɬɜɭɸɳɢɯ ɦɚɫɫ ɢ             ɧɢɹ ɞɨɩɭɫɤɚɸɬ ɩɪɨɱɬɟɧɢɟ ɤɚɤ ɫɥɟɜɚ ɧɚɩɪɚɜɨ, ɬɚɤ ɢ ɫɩɪɚɜɚ ɧɚɥɟɜɨ, ɩɨɫɤɨɥɶ-
ɫɬɟɯɢɨɦɟɬɪɢɱɟɫɤɨɝɨ ɡɚɤɨɧɚ ɢɦɟɸɬ ɜɢɞ:                                             ɤɭ ɬɭɬ ɧɟɬ ɜɵɞɟɥɟɧɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ ɩɪɟɜɪɚɳɟɧɢɹ. ɗɬɨ ɞɟɥɚɟɬ ɜ ɢɡɜɟɫɬɧɨɦ
                                                                                 ɫɦɵɫɥɟ ɭɫɥɨɜɧɵɦɢ ɩɨɧɹɬɢɹ «ɢɫɯɨɞɧɨɟ ɜɟɳɟɫɬɜɨ» ɢ «ɩɪɨɞɭɤɬ» ɪɟɚɤɰɢɢ.
                               [ B]
                         K          , CA0 – [A] = [B] – CB0.                     ɂ ɬɟ, ɢ ɞɪɭɝɢɟ, ɤɚɤ ɭɠɟ ɡɚɦɟɱɟɧɨ, ɫɨɫɭɳɟɫɬɜɭɸɬ ɜ ɪɚɜɧɨɜɟɫɧɨɣ ɫɢɫɬɟɦɟ, ɢ
                               [ A]                                              ɱɬɨ ɫɱɢɬɚɬɶ ɢɫɯɨɞɧɵɦ, ɚ ɱɬɨ ɩɪɨɞɭɤɬɨɦ – ɜɨɩɪɨɫ ɫɨɝɥɚɲɟɧɢɹ. ȿɫɥɢ ɫɬɟ-
ȼɬɨɪɨɟ ɢɡ ɧɢɯ, ɡɚɩɢɫɚɧɧɨɟ ɞɥɹ ɫɨɫɬɨɹɧɢɹ ɪɚɜɧɨɜɟɫɢɹ, ɜɵɪɚɠɚɟɬ ɫ ɨ ɯ ɪ ɚ -         ɯɢɨɦɟɬɪɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ ɩɟɪɟɩɢɫɚɬɶ ɜ ɞɪɭɝɨɣ ɨɪɢɟɧɬɚɰɢɢ, ɬɨ ɤɨɧɫɬɚɧɬɭ
ɧ ɟ ɧ ɢ ɟ ɜɟɳɟɫɬɜɚ, ɩɟɪɜɨɟ – ɪ ɚ ɫ ɩ ɪ ɟ ɞ ɟ ɥ ɟ ɧ ɢ ɟ ɜɟɳɟɫɬɜɚ ɦɟɠɞɭ ɟɝɨ ɪɚɜ-   ɪɚɜɧɨɜɟɫɢɹ ɫɥɟɞɭɟɬ ɡɚɦɟɧɢɬɶ ɨɛɪɚɬɧɨɣ ɜɟɥɢɱɢɧɨɣ K –1.
ɧɨɜɟɫɧɵɦɢ ɮɨɪɦɚɦɢ. ɂɯ ɫɨɜɦɟɫɬɧɨɟ ɪɟɲɟɧɢɟ ɞɚɟɬ:

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